Question

if the 3rd and the 9th term of an ap are 4 and -8 respectively find the 25th term​

Answer 1

-40

Step-by-step explanation:

Given -

• The 3rd term of an A.P is 4.--------(1)
• The 9rd term of the A.P is -8.------(2)

★To find -

• The 25th term.

★Solution -

$\longmapsto \rm{ \bf{a {\tiny{3}} = 4} \: \: \: \: \: \: \: \{from \: (1) \}}$

$\longmapsto \rm{ \bf{a + 2d = 4}}$

$\longmapsto \rm{ \bf \green{a = 4 - 2d} \: \: \: \: \: \: \: (3)}$

$\longmapsto \rm{ \bf{a {\tiny{9}} = - 8} \: \: \: \: \: \: \: \{from \: (2) \}}$

$\longmapsto \rm{ \bf{a + 8d = - 8} }$

${ \longmapsto \rm{ \bf{4 - 2d + 8d = - 8} \: \: \: \: \{from \: {3 \} }}}$

$\longmapsto \rm{ \bf{4 + 6d = - 8} }$

$\longmapsto \rm{ \bf{ 6d = - 8 - 4} }$

$\longmapsto \rm{ \bf{ 6d = - 12} }$

$\longmapsto \rm{ \bf{ d = \dfrac{ \cancel{ - 12} \: \: ^{ - 2} }{ \cancel6} } }$

$\longmapsto \rm{ \bf \orange{ d = - 2} \: \: \: \: \: \{putting \: in \: (3) \}}$

$\longmapsto \rm{ \bf {a = 4 - 2( - 2)} }$

$\longmapsto \rm{ \bf {a = 4 + 4} }$

$\longmapsto \rm{ \bf \pink {a = 8} }$

$\rm{Now \: { \bf{a {\tiny{25}} = a + 24d}}}$

$\longmapsto\rm{ { \bf{a {\tiny{25}} = 8 + 24( - 2)}}}$

$\longmapsto\rm{ { \bf{a {\tiny{25}} = 8 - 48}}}$

$\longmapsto\rm{ { \bf \blue{a {\tiny{25}} = - 40}}}$